Algebraic cobordism /
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| Author / Creator: | Levine, Marc, 1952- |
|---|---|
| Imprint: | Berlin : Springer, c2007. |
| Description: | xii, 244 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Springer monographs in mathematics, 1439-7382 Springer monographs in mathematics. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6284770 |
Table of Contents:
- 1. Cobordism and oriented cohomology
- 1.1. Oriented cohomology theories
- 1.2. Algebraic cobordism
- 1.3. Relations with complex cobordism
- 2. The definition of algebraic cobordism
- 2.1. Oriented Borel-Moore functors
- 2.2. Oriented functors of geometric type
- 2.3. Some elementary properties
- 2.4. The construction of algebraic cobordism
- 2.5. Some computations in algebraic cobordism
- 3. Fundamental properties of algebraic cobordism
- 3.1. Divisor classes
- 3.2. Localization
- 3.3. Transversality
- 3.4. Homotopy invariance
- 3.5. The projective bundle formula
- 3.6. The extended homotopy property
- 4. Algebraic cobordism and the Lazard ring
- 4.1. Weak homology and Chern classes
- 4.2. Algebraic cobordism and K-theory
- 4.3. The cobordism ring of a point
- 4.4. Degree formulas
- 4.5. Comparison with the Chow groups
- 5. Oriented Borel-Moore homology
- 5.1. Oriented Borel-Moore homology theories
- 5.2. Other oriented theories
- 6. Functoriality
- 6.1. Refined cobordism
- 6.2. Intersection with a pseudo-divisor
- 6.3. Intersection with a pseudo-divisor II
- 6.4. A moving lemma
- 6.5. Pull-back for l.c.i. morphisms
- 6.6. Refined pull-back and refined intersections
- 7. The universality of algebraic cobordism
- 7.1. Statement of results
- 7.2. Pull-back in Borel-Moore homology theories
- 7.3. Universality
- 7.4. Some applications
- A Resolution of singularities
- References
- Index
- Glossary of Notation